Research Article

Statistical Inference for the Kumaraswamy-Normal Distribution based on Ranked Set Sampling: An Application to Sheep Weight Data

Volume: 16 Number: 4 October 15, 2026
EN TR

Statistical Inference for the Kumaraswamy-Normal Distribution based on Ranked Set Sampling: An Application to Sheep Weight Data

Abstract

Kumaraswamy-Normal (KN) distribution is a more practical alternative to Normal distribution due to its flexible tails. This study aims to propose efficient and robust estimators for the location and scale parameters of the KN distribution. Ranked set sampling (RSS), a sampling strategy that improves efficiency while reducing cost, is used in the selection of sample units. The modified maximum likelihood (MML) methodology is employed to solve likelihood equations involving nonlinear functions of the unknown distribution parameters. The reason for preferring MML methodology is that the resulting estimators can be expressed explicitly and are robust to the outliers. A comprehensive Monte Carlo simulation study is carried out to compare the performances of the proposed estimators with those of the traditionally used simple random sampling (SRS) based maximum likelihood (ML) estimators according to bias and mean squares error (MSE) criteria. In addition, the robustness of the proposed estimators under several departures from the assumed model and their performance under imperfect ranking scenarios are also investigated. The simulation results show that RSS based MML estimators generally exhibit higher efficiency than their SRS based rivals. To highlight the practical utility of RSS based MML estimators, an application based on sheep weight data is also included.

Keywords

Kumaraswamy-Normal, Ranked set sampling, Modified likelihood, Efficiency, Monte Carlo simulation

References

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APA
Gürer, Ö., & Şenoğlu, B. (2026). Statistical Inference for the Kumaraswamy-Normal Distribution based on Ranked Set Sampling: An Application to Sheep Weight Data. Karadeniz Fen Bilimleri Dergisi, 16(4), 1810-1831. https://doi.org/10.31466/kfbd.1918873
AMA
1.Gürer Ö, Şenoğlu B. Statistical Inference for the Kumaraswamy-Normal Distribution based on Ranked Set Sampling: An Application to Sheep Weight Data. KFBD. 2026;16(4):1810-1831. doi:10.31466/kfbd.1918873
Chicago
Gürer, Özge, and Birdal Şenoğlu. 2026. “Statistical Inference for the Kumaraswamy-Normal Distribution Based on Ranked Set Sampling: An Application to Sheep Weight Data”. Karadeniz Fen Bilimleri Dergisi 16 (4): 1810-31. https://doi.org/10.31466/kfbd.1918873.
EndNote
Gürer Ö, Şenoğlu B (October 1, 2026) Statistical Inference for the Kumaraswamy-Normal Distribution based on Ranked Set Sampling: An Application to Sheep Weight Data. Karadeniz Fen Bilimleri Dergisi 16 4 1810–1831.
IEEE
[1]Ö. Gürer and B. Şenoğlu, “Statistical Inference for the Kumaraswamy-Normal Distribution based on Ranked Set Sampling: An Application to Sheep Weight Data”, KFBD, vol. 16, no. 4, pp. 1810–1831, Oct. 2026, doi: 10.31466/kfbd.1918873.
ISNAD
Gürer, Özge - Şenoğlu, Birdal. “Statistical Inference for the Kumaraswamy-Normal Distribution Based on Ranked Set Sampling: An Application to Sheep Weight Data”. Karadeniz Fen Bilimleri Dergisi 16/4 (October 1, 2026): 1810-1831. https://doi.org/10.31466/kfbd.1918873.
JAMA
1.Gürer Ö, Şenoğlu B. Statistical Inference for the Kumaraswamy-Normal Distribution based on Ranked Set Sampling: An Application to Sheep Weight Data. KFBD. 2026;16:1810–1831.
MLA
Gürer, Özge, and Birdal Şenoğlu. “Statistical Inference for the Kumaraswamy-Normal Distribution Based on Ranked Set Sampling: An Application to Sheep Weight Data”. Karadeniz Fen Bilimleri Dergisi, vol. 16, no. 4, Oct. 2026, pp. 1810-31, doi:10.31466/kfbd.1918873.
Vancouver
1.Özge Gürer, Birdal Şenoğlu. Statistical Inference for the Kumaraswamy-Normal Distribution based on Ranked Set Sampling: An Application to Sheep Weight Data. KFBD. 2026 Oct. 1;16(4):1810-31. doi:10.31466/kfbd.1918873